1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 137,634 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 137,624 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     61
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     91
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     44
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     35
## 67   2020-05-06          East of England     30
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     24
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     16
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     15
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     14
## 94   2020-06-02          East of England     12
## 95   2020-06-03          East of England      7
## 96   2020-06-04          East of England      4
## 97   2020-06-05          East of England      4
## 98   2020-06-06          East of England      1
## 99   2020-03-01                   London      0
## 100  2020-03-02                   London      0
## 101  2020-03-03                   London      0
## 102  2020-03-04                   London      0
## 103  2020-03-05                   London      0
## 104  2020-03-06                   London      1
## 105  2020-03-07                   London      1
## 106  2020-03-08                   London      0
## 107  2020-03-09                   London      1
## 108  2020-03-10                   London      0
## 109  2020-03-11                   London      7
## 110  2020-03-12                   London      6
## 111  2020-03-13                   London     10
## 112  2020-03-14                   London     14
## 113  2020-03-15                   London     10
## 114  2020-03-16                   London     17
## 115  2020-03-17                   London     25
## 116  2020-03-18                   London     31
## 117  2020-03-19                   London     25
## 118  2020-03-20                   London     45
## 119  2020-03-21                   London     50
## 120  2020-03-22                   London     54
## 121  2020-03-23                   London     64
## 122  2020-03-24                   London     87
## 123  2020-03-25                   London    113
## 124  2020-03-26                   London    130
## 125  2020-03-27                   London    130
## 126  2020-03-28                   London    122
## 127  2020-03-29                   London    147
## 128  2020-03-30                   London    150
## 129  2020-03-31                   London    181
## 130  2020-04-01                   London    202
## 131  2020-04-02                   London    190
## 132  2020-04-03                   London    196
## 133  2020-04-04                   London    230
## 134  2020-04-05                   London    195
## 135  2020-04-06                   London    198
## 136  2020-04-07                   London    219
## 137  2020-04-08                   London    238
## 138  2020-04-09                   London    205
## 139  2020-04-10                   London    170
## 140  2020-04-11                   London    176
## 141  2020-04-12                   London    158
## 142  2020-04-13                   London    166
## 143  2020-04-14                   London    143
## 144  2020-04-15                   London    142
## 145  2020-04-16                   London    139
## 146  2020-04-17                   London     99
## 147  2020-04-18                   London    101
## 148  2020-04-19                   London    102
## 149  2020-04-20                   London     95
## 150  2020-04-21                   London     95
## 151  2020-04-22                   London    108
## 152  2020-04-23                   London     77
## 153  2020-04-24                   London     71
## 154  2020-04-25                   London     57
## 155  2020-04-26                   London     53
## 156  2020-04-27                   London     51
## 157  2020-04-28                   London     43
## 158  2020-04-29                   London     44
## 159  2020-04-30                   London     39
## 160  2020-05-01                   London     41
## 161  2020-05-02                   London     40
## 162  2020-05-03                   London     36
## 163  2020-05-04                   London     29
## 164  2020-05-05                   London     25
## 165  2020-05-06                   London     36
## 166  2020-05-07                   London     37
## 167  2020-05-08                   London     29
## 168  2020-05-09                   London     23
## 169  2020-05-10                   London     26
## 170  2020-05-11                   London     18
## 171  2020-05-12                   London     18
## 172  2020-05-13                   London     16
## 173  2020-05-14                   London     20
## 174  2020-05-15                   London     18
## 175  2020-05-16                   London     14
## 176  2020-05-17                   London     15
## 177  2020-05-18                   London      9
## 178  2020-05-19                   London     13
## 179  2020-05-20                   London     19
## 180  2020-05-21                   London     12
## 181  2020-05-22                   London     10
## 182  2020-05-23                   London      6
## 183  2020-05-24                   London      7
## 184  2020-05-25                   London      8
## 185  2020-05-26                   London     12
## 186  2020-05-27                   London      7
## 187  2020-05-28                   London      7
## 188  2020-05-29                   London      7
## 189  2020-05-30                   London     12
## 190  2020-05-31                   London      6
## 191  2020-06-01                   London      8
## 192  2020-06-02                   London      6
## 193  2020-06-03                   London      5
## 194  2020-06-04                   London      6
## 195  2020-06-05                   London      2
## 196  2020-06-06                   London      0
## 197  2020-03-01                 Midlands      0
## 198  2020-03-02                 Midlands      0
## 199  2020-03-03                 Midlands      1
## 200  2020-03-04                 Midlands      0
## 201  2020-03-05                 Midlands      0
## 202  2020-03-06                 Midlands      0
## 203  2020-03-07                 Midlands      0
## 204  2020-03-08                 Midlands      3
## 205  2020-03-09                 Midlands      1
## 206  2020-03-10                 Midlands      0
## 207  2020-03-11                 Midlands      2
## 208  2020-03-12                 Midlands      6
## 209  2020-03-13                 Midlands      5
## 210  2020-03-14                 Midlands      4
## 211  2020-03-15                 Midlands      5
## 212  2020-03-16                 Midlands     11
## 213  2020-03-17                 Midlands      8
## 214  2020-03-18                 Midlands     13
## 215  2020-03-19                 Midlands      8
## 216  2020-03-20                 Midlands     28
## 217  2020-03-21                 Midlands     13
## 218  2020-03-22                 Midlands     31
## 219  2020-03-23                 Midlands     33
## 220  2020-03-24                 Midlands     41
## 221  2020-03-25                 Midlands     48
## 222  2020-03-26                 Midlands     64
## 223  2020-03-27                 Midlands     72
## 224  2020-03-28                 Midlands     89
## 225  2020-03-29                 Midlands     92
## 226  2020-03-30                 Midlands     90
## 227  2020-03-31                 Midlands    123
## 228  2020-04-01                 Midlands    140
## 229  2020-04-02                 Midlands    142
## 230  2020-04-03                 Midlands    124
## 231  2020-04-04                 Midlands    151
## 232  2020-04-05                 Midlands    164
## 233  2020-04-06                 Midlands    140
## 234  2020-04-07                 Midlands    123
## 235  2020-04-08                 Midlands    186
## 236  2020-04-09                 Midlands    139
## 237  2020-04-10                 Midlands    127
## 238  2020-04-11                 Midlands    142
## 239  2020-04-12                 Midlands    139
## 240  2020-04-13                 Midlands    120
## 241  2020-04-14                 Midlands    116
## 242  2020-04-15                 Midlands    147
## 243  2020-04-16                 Midlands    102
## 244  2020-04-17                 Midlands    118
## 245  2020-04-18                 Midlands    115
## 246  2020-04-19                 Midlands     92
## 247  2020-04-20                 Midlands    107
## 248  2020-04-21                 Midlands     86
## 249  2020-04-22                 Midlands     78
## 250  2020-04-23                 Midlands    103
## 251  2020-04-24                 Midlands     79
## 252  2020-04-25                 Midlands     72
## 253  2020-04-26                 Midlands     81
## 254  2020-04-27                 Midlands     74
## 255  2020-04-28                 Midlands     68
## 256  2020-04-29                 Midlands     53
## 257  2020-04-30                 Midlands     56
## 258  2020-05-01                 Midlands     64
## 259  2020-05-02                 Midlands     51
## 260  2020-05-03                 Midlands     52
## 261  2020-05-04                 Midlands     61
## 262  2020-05-05                 Midlands     58
## 263  2020-05-06                 Midlands     59
## 264  2020-05-07                 Midlands     48
## 265  2020-05-08                 Midlands     34
## 266  2020-05-09                 Midlands     37
## 267  2020-05-10                 Midlands     41
## 268  2020-05-11                 Midlands     33
## 269  2020-05-12                 Midlands     45
## 270  2020-05-13                 Midlands     39
## 271  2020-05-14                 Midlands     36
## 272  2020-05-15                 Midlands     40
## 273  2020-05-16                 Midlands     34
## 274  2020-05-17                 Midlands     31
## 275  2020-05-18                 Midlands     34
## 276  2020-05-19                 Midlands     34
## 277  2020-05-20                 Midlands     36
## 278  2020-05-21                 Midlands     32
## 279  2020-05-22                 Midlands     26
## 280  2020-05-23                 Midlands     31
## 281  2020-05-24                 Midlands     19
## 282  2020-05-25                 Midlands     25
## 283  2020-05-26                 Midlands     32
## 284  2020-05-27                 Midlands     29
## 285  2020-05-28                 Midlands     27
## 286  2020-05-29                 Midlands     20
## 287  2020-05-30                 Midlands     20
## 288  2020-05-31                 Midlands     20
## 289  2020-06-01                 Midlands     20
## 290  2020-06-02                 Midlands     20
## 291  2020-06-03                 Midlands     21
## 292  2020-06-04                 Midlands     11
## 293  2020-06-05                 Midlands     13
## 294  2020-06-06                 Midlands      2
## 295  2020-03-01 North East and Yorkshire      0
## 296  2020-03-02 North East and Yorkshire      0
## 297  2020-03-03 North East and Yorkshire      0
## 298  2020-03-04 North East and Yorkshire      0
## 299  2020-03-05 North East and Yorkshire      0
## 300  2020-03-06 North East and Yorkshire      0
## 301  2020-03-07 North East and Yorkshire      0
## 302  2020-03-08 North East and Yorkshire      0
## 303  2020-03-09 North East and Yorkshire      0
## 304  2020-03-10 North East and Yorkshire      0
## 305  2020-03-11 North East and Yorkshire      0
## 306  2020-03-12 North East and Yorkshire      0
## 307  2020-03-13 North East and Yorkshire      0
## 308  2020-03-14 North East and Yorkshire      0
## 309  2020-03-15 North East and Yorkshire      2
## 310  2020-03-16 North East and Yorkshire      3
## 311  2020-03-17 North East and Yorkshire      1
## 312  2020-03-18 North East and Yorkshire      2
## 313  2020-03-19 North East and Yorkshire      6
## 314  2020-03-20 North East and Yorkshire      5
## 315  2020-03-21 North East and Yorkshire      6
## 316  2020-03-22 North East and Yorkshire      7
## 317  2020-03-23 North East and Yorkshire      9
## 318  2020-03-24 North East and Yorkshire      8
## 319  2020-03-25 North East and Yorkshire     18
## 320  2020-03-26 North East and Yorkshire     21
## 321  2020-03-27 North East and Yorkshire     28
## 322  2020-03-28 North East and Yorkshire     35
## 323  2020-03-29 North East and Yorkshire     38
## 324  2020-03-30 North East and Yorkshire     64
## 325  2020-03-31 North East and Yorkshire     60
## 326  2020-04-01 North East and Yorkshire     67
## 327  2020-04-02 North East and Yorkshire     74
## 328  2020-04-03 North East and Yorkshire    100
## 329  2020-04-04 North East and Yorkshire    105
## 330  2020-04-05 North East and Yorkshire     92
## 331  2020-04-06 North East and Yorkshire     96
## 332  2020-04-07 North East and Yorkshire    102
## 333  2020-04-08 North East and Yorkshire    107
## 334  2020-04-09 North East and Yorkshire    111
## 335  2020-04-10 North East and Yorkshire    117
## 336  2020-04-11 North East and Yorkshire     98
## 337  2020-04-12 North East and Yorkshire     84
## 338  2020-04-13 North East and Yorkshire     94
## 339  2020-04-14 North East and Yorkshire    107
## 340  2020-04-15 North East and Yorkshire     96
## 341  2020-04-16 North East and Yorkshire    103
## 342  2020-04-17 North East and Yorkshire     88
## 343  2020-04-18 North East and Yorkshire     95
## 344  2020-04-19 North East and Yorkshire     88
## 345  2020-04-20 North East and Yorkshire    100
## 346  2020-04-21 North East and Yorkshire     76
## 347  2020-04-22 North East and Yorkshire     84
## 348  2020-04-23 North East and Yorkshire     62
## 349  2020-04-24 North East and Yorkshire     72
## 350  2020-04-25 North East and Yorkshire     69
## 351  2020-04-26 North East and Yorkshire     65
## 352  2020-04-27 North East and Yorkshire     65
## 353  2020-04-28 North East and Yorkshire     57
## 354  2020-04-29 North East and Yorkshire     69
## 355  2020-04-30 North East and Yorkshire     57
## 356  2020-05-01 North East and Yorkshire     64
## 357  2020-05-02 North East and Yorkshire     48
## 358  2020-05-03 North East and Yorkshire     40
## 359  2020-05-04 North East and Yorkshire     49
## 360  2020-05-05 North East and Yorkshire     40
## 361  2020-05-06 North East and Yorkshire     50
## 362  2020-05-07 North East and Yorkshire     45
## 363  2020-05-08 North East and Yorkshire     42
## 364  2020-05-09 North East and Yorkshire     44
## 365  2020-05-10 North East and Yorkshire     40
## 366  2020-05-11 North East and Yorkshire     29
## 367  2020-05-12 North East and Yorkshire     27
## 368  2020-05-13 North East and Yorkshire     28
## 369  2020-05-14 North East and Yorkshire     30
## 370  2020-05-15 North East and Yorkshire     32
## 371  2020-05-16 North East and Yorkshire     35
## 372  2020-05-17 North East and Yorkshire     26
## 373  2020-05-18 North East and Yorkshire     29
## 374  2020-05-19 North East and Yorkshire     27
## 375  2020-05-20 North East and Yorkshire     21
## 376  2020-05-21 North East and Yorkshire     33
## 377  2020-05-22 North East and Yorkshire     22
## 378  2020-05-23 North East and Yorkshire     18
## 379  2020-05-24 North East and Yorkshire     23
## 380  2020-05-25 North East and Yorkshire     21
## 381  2020-05-26 North East and Yorkshire     21
## 382  2020-05-27 North East and Yorkshire     18
## 383  2020-05-28 North East and Yorkshire     19
## 384  2020-05-29 North East and Yorkshire     24
## 385  2020-05-30 North East and Yorkshire     20
## 386  2020-05-31 North East and Yorkshire     18
## 387  2020-06-01 North East and Yorkshire     15
## 388  2020-06-02 North East and Yorkshire     22
## 389  2020-06-03 North East and Yorkshire     21
## 390  2020-06-04 North East and Yorkshire     15
## 391  2020-06-05 North East and Yorkshire     12
## 392  2020-06-06 North East and Yorkshire     11
## 393  2020-03-01               North West      0
## 394  2020-03-02               North West      0
## 395  2020-03-03               North West      0
## 396  2020-03-04               North West      0
## 397  2020-03-05               North West      1
## 398  2020-03-06               North West      0
## 399  2020-03-07               North West      0
## 400  2020-03-08               North West      1
## 401  2020-03-09               North West      0
## 402  2020-03-10               North West      0
## 403  2020-03-11               North West      0
## 404  2020-03-12               North West      2
## 405  2020-03-13               North West      3
## 406  2020-03-14               North West      1
## 407  2020-03-15               North West      4
## 408  2020-03-16               North West      2
## 409  2020-03-17               North West      4
## 410  2020-03-18               North West      6
## 411  2020-03-19               North West      7
## 412  2020-03-20               North West     10
## 413  2020-03-21               North West     11
## 414  2020-03-22               North West     13
## 415  2020-03-23               North West     16
## 416  2020-03-24               North West     21
## 417  2020-03-25               North West     21
## 418  2020-03-26               North West     29
## 419  2020-03-27               North West     35
## 420  2020-03-28               North West     28
## 421  2020-03-29               North West     46
## 422  2020-03-30               North West     67
## 423  2020-03-31               North West     52
## 424  2020-04-01               North West     86
## 425  2020-04-02               North West     96
## 426  2020-04-03               North West     95
## 427  2020-04-04               North West     98
## 428  2020-04-05               North West    102
## 429  2020-04-06               North West    100
## 430  2020-04-07               North West    133
## 431  2020-04-08               North West    127
## 432  2020-04-09               North West    119
## 433  2020-04-10               North West    117
## 434  2020-04-11               North West    138
## 435  2020-04-12               North West    126
## 436  2020-04-13               North West    127
## 437  2020-04-14               North West    131
## 438  2020-04-15               North West    114
## 439  2020-04-16               North West    134
## 440  2020-04-17               North West     98
## 441  2020-04-18               North West    113
## 442  2020-04-19               North West     71
## 443  2020-04-20               North West     83
## 444  2020-04-21               North West     76
## 445  2020-04-22               North West     86
## 446  2020-04-23               North West     85
## 447  2020-04-24               North West     66
## 448  2020-04-25               North West     65
## 449  2020-04-26               North West     55
## 450  2020-04-27               North West     54
## 451  2020-04-28               North West     57
## 452  2020-04-29               North West     62
## 453  2020-04-30               North West     59
## 454  2020-05-01               North West     44
## 455  2020-05-02               North West     56
## 456  2020-05-03               North West     55
## 457  2020-05-04               North West     48
## 458  2020-05-05               North West     48
## 459  2020-05-06               North West     44
## 460  2020-05-07               North West     49
## 461  2020-05-08               North West     42
## 462  2020-05-09               North West     30
## 463  2020-05-10               North West     41
## 464  2020-05-11               North West     34
## 465  2020-05-12               North West     38
## 466  2020-05-13               North West     24
## 467  2020-05-14               North West     26
## 468  2020-05-15               North West     33
## 469  2020-05-16               North West     32
## 470  2020-05-17               North West     24
## 471  2020-05-18               North West     30
## 472  2020-05-19               North West     35
## 473  2020-05-20               North West     25
## 474  2020-05-21               North West     25
## 475  2020-05-22               North West     26
## 476  2020-05-23               North West     31
## 477  2020-05-24               North West     26
## 478  2020-05-25               North West     31
## 479  2020-05-26               North West     27
## 480  2020-05-27               North West     27
## 481  2020-05-28               North West     27
## 482  2020-05-29               North West     19
## 483  2020-05-30               North West     17
## 484  2020-05-31               North West     13
## 485  2020-06-01               North West     12
## 486  2020-06-02               North West     25
## 487  2020-06-03               North West     17
## 488  2020-06-04               North West     17
## 489  2020-06-05               North West      8
## 490  2020-06-06               North West      2
## 491  2020-03-01               South East      0
## 492  2020-03-02               South East      0
## 493  2020-03-03               South East      1
## 494  2020-03-04               South East      0
## 495  2020-03-05               South East      1
## 496  2020-03-06               South East      0
## 497  2020-03-07               South East      0
## 498  2020-03-08               South East      1
## 499  2020-03-09               South East      1
## 500  2020-03-10               South East      1
## 501  2020-03-11               South East      1
## 502  2020-03-12               South East      0
## 503  2020-03-13               South East      1
## 504  2020-03-14               South East      1
## 505  2020-03-15               South East      5
## 506  2020-03-16               South East      8
## 507  2020-03-17               South East      7
## 508  2020-03-18               South East     10
## 509  2020-03-19               South East      9
## 510  2020-03-20               South East     14
## 511  2020-03-21               South East      7
## 512  2020-03-22               South East     25
## 513  2020-03-23               South East     20
## 514  2020-03-24               South East     22
## 515  2020-03-25               South East     29
## 516  2020-03-26               South East     34
## 517  2020-03-27               South East     34
## 518  2020-03-28               South East     36
## 519  2020-03-29               South East     54
## 520  2020-03-30               South East     58
## 521  2020-03-31               South East     65
## 522  2020-04-01               South East     65
## 523  2020-04-02               South East     55
## 524  2020-04-03               South East     72
## 525  2020-04-04               South East     80
## 526  2020-04-05               South East     82
## 527  2020-04-06               South East     88
## 528  2020-04-07               South East    100
## 529  2020-04-08               South East     83
## 530  2020-04-09               South East    104
## 531  2020-04-10               South East     88
## 532  2020-04-11               South East     88
## 533  2020-04-12               South East     88
## 534  2020-04-13               South East     84
## 535  2020-04-14               South East     65
## 536  2020-04-15               South East     72
## 537  2020-04-16               South East     56
## 538  2020-04-17               South East     86
## 539  2020-04-18               South East     57
## 540  2020-04-19               South East     70
## 541  2020-04-20               South East     85
## 542  2020-04-21               South East     50
## 543  2020-04-22               South East     54
## 544  2020-04-23               South East     57
## 545  2020-04-24               South East     64
## 546  2020-04-25               South East     51
## 547  2020-04-26               South East     51
## 548  2020-04-27               South East     40
## 549  2020-04-28               South East     40
## 550  2020-04-29               South East     47
## 551  2020-04-30               South East     29
## 552  2020-05-01               South East     37
## 553  2020-05-02               South East     36
## 554  2020-05-03               South East     17
## 555  2020-05-04               South East     35
## 556  2020-05-05               South East     29
## 557  2020-05-06               South East     25
## 558  2020-05-07               South East     27
## 559  2020-05-08               South East     26
## 560  2020-05-09               South East     28
## 561  2020-05-10               South East     19
## 562  2020-05-11               South East     25
## 563  2020-05-12               South East     27
## 564  2020-05-13               South East     18
## 565  2020-05-14               South East     32
## 566  2020-05-15               South East     24
## 567  2020-05-16               South East     22
## 568  2020-05-17               South East     17
## 569  2020-05-18               South East     22
## 570  2020-05-19               South East     12
## 571  2020-05-20               South East     22
## 572  2020-05-21               South East     14
## 573  2020-05-22               South East     17
## 574  2020-05-23               South East     19
## 575  2020-05-24               South East     16
## 576  2020-05-25               South East     13
## 577  2020-05-26               South East     17
## 578  2020-05-27               South East     17
## 579  2020-05-28               South East     12
## 580  2020-05-29               South East     17
## 581  2020-05-30               South East      8
## 582  2020-05-31               South East     10
## 583  2020-06-01               South East     11
## 584  2020-06-02               South East      9
## 585  2020-06-03               South East     15
## 586  2020-06-04               South East      8
## 587  2020-06-05               South East      6
## 588  2020-06-06               South East      0
## 589  2020-03-01               South West      0
## 590  2020-03-02               South West      0
## 591  2020-03-03               South West      0
## 592  2020-03-04               South West      0
## 593  2020-03-05               South West      0
## 594  2020-03-06               South West      0
## 595  2020-03-07               South West      0
## 596  2020-03-08               South West      0
## 597  2020-03-09               South West      0
## 598  2020-03-10               South West      0
## 599  2020-03-11               South West      1
## 600  2020-03-12               South West      0
## 601  2020-03-13               South West      0
## 602  2020-03-14               South West      1
## 603  2020-03-15               South West      0
## 604  2020-03-16               South West      0
## 605  2020-03-17               South West      2
## 606  2020-03-18               South West      2
## 607  2020-03-19               South West      5
## 608  2020-03-20               South West      3
## 609  2020-03-21               South West      6
## 610  2020-03-22               South West      9
## 611  2020-03-23               South West      9
## 612  2020-03-24               South West      7
## 613  2020-03-25               South West      9
## 614  2020-03-26               South West     11
## 615  2020-03-27               South West     13
## 616  2020-03-28               South West     21
## 617  2020-03-29               South West     18
## 618  2020-03-30               South West     23
## 619  2020-03-31               South West     23
## 620  2020-04-01               South West     22
## 621  2020-04-02               South West     23
## 622  2020-04-03               South West     30
## 623  2020-04-04               South West     42
## 624  2020-04-05               South West     32
## 625  2020-04-06               South West     34
## 626  2020-04-07               South West     39
## 627  2020-04-08               South West     47
## 628  2020-04-09               South West     24
## 629  2020-04-10               South West     46
## 630  2020-04-11               South West     43
## 631  2020-04-12               South West     23
## 632  2020-04-13               South West     27
## 633  2020-04-14               South West     24
## 634  2020-04-15               South West     32
## 635  2020-04-16               South West     29
## 636  2020-04-17               South West     33
## 637  2020-04-18               South West     25
## 638  2020-04-19               South West     31
## 639  2020-04-20               South West     26
## 640  2020-04-21               South West     26
## 641  2020-04-22               South West     22
## 642  2020-04-23               South West     17
## 643  2020-04-24               South West     19
## 644  2020-04-25               South West     15
## 645  2020-04-26               South West     27
## 646  2020-04-27               South West     13
## 647  2020-04-28               South West     17
## 648  2020-04-29               South West     15
## 649  2020-04-30               South West     26
## 650  2020-05-01               South West      6
## 651  2020-05-02               South West      7
## 652  2020-05-03               South West     10
## 653  2020-05-04               South West     16
## 654  2020-05-05               South West     14
## 655  2020-05-06               South West     18
## 656  2020-05-07               South West     16
## 657  2020-05-08               South West      6
## 658  2020-05-09               South West     11
## 659  2020-05-10               South West      5
## 660  2020-05-11               South West      8
## 661  2020-05-12               South West      7
## 662  2020-05-13               South West      7
## 663  2020-05-14               South West      6
## 664  2020-05-15               South West      4
## 665  2020-05-16               South West      4
## 666  2020-05-17               South West      6
## 667  2020-05-18               South West      4
## 668  2020-05-19               South West      6
## 669  2020-05-20               South West      1
## 670  2020-05-21               South West      9
## 671  2020-05-22               South West      6
## 672  2020-05-23               South West      6
## 673  2020-05-24               South West      3
## 674  2020-05-25               South West      8
## 675  2020-05-26               South West     11
## 676  2020-05-27               South West      5
## 677  2020-05-28               South West      9
## 678  2020-05-29               South West      4
## 679  2020-05-30               South West      3
## 680  2020-05-31               South West      2
## 681  2020-06-01               South West      6
## 682  2020-06-02               South West      2
## 683  2020-06-03               South West      5
## 684  2020-06-04               South West      1
## 685  2020-06-05               South West      1
## 686  2020-06-06               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-07"

The completion date of the NHS Pathways data is Sunday 07 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -7.6046  -1.9041   0.3866   1.7380   4.5943  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 5.127e+00  5.061e-02  101.31   <2e-16 ***
## note_lag    1.016e-05  4.834e-07   21.02   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 7.090473)
## 
##     Null deviance: 3409.25  on 36  degrees of freedom
## Residual deviance:  254.21  on 35  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##   168.54197     1.00001
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 152.484417 185.946533
## note_lag      1.000009   1.000011

Rsq(lag_mod)
## [1] 0.9254348

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Thu Apr 30 18:25:59 PDT 2020; root:xnu-6153.121.1~7/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1666.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.8     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.13             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.4.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.1       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.28       
## [13] jsonlite_1.6.1    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.7   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.4.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.14         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.5.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.2    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0